Application of a novel nonlinear multivariate grey Bernoulli model to predict the tourist income of China

The nonlinear grey Bernoulli model, which is often called the NGBM(1, 1), appeals considerable interest of research due to its effectiveness in time series forecasting. The success of the NGBM(1, 1) model proves that the nonlinear Bernoulli equation can be efficient to build grey prediction models. This paper is mainly aiming at building a more general nonlinear grey prediction model based on the Bernoulli equation and the modelling procedures of the GMC(1, n), which is called the nonlinear grey Bernoulli multivariate model, abbreviated as the NGBMC(1, n). The NGBMC(1, n) can be converted to the NGBM(1, 1) and the GMC(1, n) with different power parameters, thus it can be regarded as an extension of these models. Two case studies of forecasting the domestic income and foreign currency earning have been carried out to validate the effectiveness of the NGBMC(1, n) model, comparing to the novel linear multivariate grey models, including the GMC(1, n), DGM(1, n) and RDGM(1, n), and the classical ARIMA model. The advantages of the NGBMC(1, n) model in nonlinear time series forecasting over the existing linear models have been shown in the numerical results.